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| Mirrors > Home > MPE Home > Th. List > lveclmod | Structured version Visualization version GIF version | ||
| Description: A left vector space is a left module. (Contributed by NM, 9-Dec-2013.) |
| Ref | Expression |
|---|---|
| lveclmod | ⊢ (𝑊 ∈ LVec → 𝑊 ∈ LMod) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqid 2737 | . . 3 ⊢ (Scalar‘𝑊) = (Scalar‘𝑊) | |
| 2 | 1 | islvec 21103 | . 2 ⊢ (𝑊 ∈ LVec ↔ (𝑊 ∈ LMod ∧ (Scalar‘𝑊) ∈ DivRing)) |
| 3 | 2 | simplbi 497 | 1 ⊢ (𝑊 ∈ LVec → 𝑊 ∈ LMod) |
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